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3 years ago

Which table represents a linear function?

Mathematics

2 answers:

Alex73 [517]3 years ago

3 0

First one is your answer
x y
1 5
2 10
3 15
4 20
5 25

mylen [45]3 years ago

3 0

<h2>Answer:</h2>

The table which represents a linear function is:

x y

1 5

2 10

3 15

4 20

5 25

<h2>Step-by-step explanation:</h2>

The table of x and y values represent a linear function if for each equal increase in the x-value there is an equal increase/decrease in the y-value.

The table of values is:

x y

1 5

2 10

3 15

4 20

5 25

In this table the x-value is increasing by a constant value 1.

( since,

2-1=1

3-2=1

4-3=1

5-4=1 )

and the y-value is also increasing by a constant value 5.

( since,

10-5=5

15-10=5

20-15=5

and 25-20=5 )

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Of the total population of American households, including older Americans and perhaps some not so old, 17.3% receive retirement

Alex Ar [27]

Answer:

47.54% probability that more than 20 households but fewer than 35 households receive a retirement income

Step-by-step explanation:

We use the binomial aproxiation to the normal to solve this question.

Binomial probability distribution

Probability of exactly x sucesses on n repeated trials, with p probability.

Can be approximated to a normal distribution, using the expected value and the standard deviation.

The expected value of the binomial distribution is:

$E(X) = np$

The standard deviation of the binomial distribution is:

$\sqrt{V(X)} = \sqrt{np(1-p)}$

Normal probability distribution

Problems of normally distributed samples can be solved using the z-score formula.

In a set with mean $\mu$ and standard deviation $\sigma$ , the zscore of a measure X is given by:

$Z = \frac{X - \mu}{\sigma}$

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

When we are approximating a binomial distribution to a normal one, we have that $\mu = E(X)$ , $\sigma = \sqrt{V(X)}$ .

In this problem, we have that:

$p = 0.173, n = 120$ . So

$\mu = E(X) = np = 120*0.173 = 20.76$

$\sigma = \sqrt{V(X)} = \sqrt{np(1-p)} = \sqrt{120*0.173*0.827} = 4.14$

In a random sample of 120 households, what is the probability that more than 20 households but fewer than 35 households receive a retirement income?

We are working with discrete values, so this is the pvalue of Z when X = 35-1 = 34 subtracted by the pvalue of Z when X = 20 + 1 = 21.

X = 34

$Z = \frac{X - \mu}{\sigma}$

$Z = \frac{34 - 20.76}{4.14}$

$Z = 3.2$

$Z = 3.2$ has a pvalue of 0.9993

X = 21

$Z = \frac{X - \mu}{\sigma}$

$Z = \frac{21 - 20.76}{4.14}$

$Z = 0.06$

$Z = 0.06$ has a pvalue of 0.5239

0.9993 - 0.5239 = 0.4754

47.54% probability that more than 20 households but fewer than 35 households receive a retirement income

6 0

3 years ago

What does x equal in the solution

TiliK225 [7]

Answer: 2

Step-by-step explanation:

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3 years ago

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marusya05 [52]

Using the binomial distribution, it is found that the number of students that would be expected to select a gold-wrapped candy from the bag is given by:

B. 5 students

The candies are chosen with replacement, which means that for each student, the probability of choosing a gold wrapped candy is independent of any other student, hence the binomial distribution is used.

<h3>What is the binomial distribution?</h3>

The <em>binomial distribution</em> is the <u>probability of exactly x successes on n repeated trials, with p probability of a success on each trial</u>.

The expected value of the binomial distribution is:

$E(X) = np$

In this problem: